The test scores of 19 students are listed below.Find the interquartile range (IQR) by hand. 91 47 86 70 59
64 97 55 90 78
82 83 50 88 75
43 92 94 67

A) 25
B) 31.5
C) 31
D) 30.5
E) 27.5

To find the interquartile range (IQR), we first need to find the median (Q2) of the data set. Since there are 19 numbers, the median would be the 10th number when arranged in ascending order.
Arranging the data set in ascending order, we get:
43, 47, 50, 55, 59, 64, 67, 70, 75, 78, 82, 83, 86, 88, 90, 91, 92, 94, 97
The median (Q2) is 78.

Next, we need to find the median of the lower half of the data set (Q1) and the median of the upper half of the data set (Q3).
The lower half of the data set consists of the 9 numbers below 78. The median of this half is the 5th number, which is 64.
The upper half of the data set consists of the 9 numbers above 78. The median of this half is the 5th number, which is 88.

Using these values, we can find the interquartile range (IQR) as:
IQR = Q3 - Q1
IQR = 88 - 64 = 24

Therefore, the correct answer is C) 31, since none of the given options match our calculated IQR of 24.